Find the average rate of change of gx 7x2 on the interval

Find the average rate of change of g(x) = 7x2 + on the interval [-3,1] 3 Preview Points possible: 2

Solution

a) given g(x)=7x²+(2/x³)

average rate of change in interval [-3,1] is [g(1)-g(-3)]/(1-(-3))

= [7(1)²+(2/(1)³) -7(-3)²-(2/(-3)³) ]/(4)

= [7+2 -(7*9) +(2/27) ]/(4)

=(-1456/27)/4

=-364/27

average rate of change in interval [-3,1] =-364/27=-13.48

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f(x)=x²+4x

rate of change in interval [-2,-2+h] is [f(-2+h) -f(-2)]/(-2+h -(-2))

= [(-2+h)²+4(-2+h) -(-2)²-4(-2)]/(h )

= [4-4h+h² -8+4h -4 +8)]/(h )

= [h²]/(h )

=h

average rate of change =h